Tuesday, July 22, 2014

TMC #14 GWWG – Annotated References: the research on explicit teaching of exploratory talk

OK, last summarizing post before I have to get packing.

Here is the background research on ‘exploratory talk. Once again, please note that this is NOT required reading!  Recreational reading only! So please don't freak out!  :)

I wanted to provide links and titles to valuable materials.

These are listed in order of relevance to the Group Work Working Group morning session — they are not in formal bibliographical form.

Shell Centre,  MAP PD: Students Working Collaboratively (PD Module 5)
An adequate introduction, with pointers to some of the major reseach on exploratory talk in the math classroom. PD module on using talk in the math classroom. There are two parts to download: the overview and the “handouts for teachers.” The Handouts for Teachers is more useful than the overview, but you kind of need both to get started.

Neil Mercer and Steve Hodgkinson, editors, Exploring Talk in School
The richest single source of research on cultivating exploratory talk, though many of the chapters I found most useful are available on the internet.

Douglas Barnes, “Exploratory Talk for Learning” (chapter 1 in Exploring Talk in School, but downloadable PDF here)
Barnes is the research who originally pioneered the concept of exploratory talk as distinguished from cumulative talk and disputational talk. Everybody else’s work builds on his.

Neil Mercer and Lyn Dawes, “The value of exploratory talk” (chapter 4 in Exploring Talk in School, but downloadable PDF here)
An explanation of the need for differing kinds of talk in the classroom (asymmetrical teacher-student talk as well as symmetric student-student or peer talk). Makes a strong case for doing the work to intentionally raise the level of symmetrical talk to make group work effective and meaningful.

Lyn Dawes, The Essential Speaking and Listening,  Chapter 2: “Talking Points” (downloadable PDF here). 
Overview of her original strategy for using the “Talking Points” activity structure to encourage students to develop what Barnes referred to as “an open and hypothetical style of learning.” This is what I used as the basis for developing my own version of the Talking Points activity.

Thinking Together
How can children be explicitly enabled to use talk more effectively as a tool for reasoning? The Thinking Together program was founded to address this specific question. A freely available, evidence-based interventional program of three talk lessons plus supporting materials, developed by University of Cambridge Faculty of Education researchers (led by Mercer and Dawes) as “a dialogue-based approach to the development of children’s thinking and learning.” It has been widely implemented in the U.K. as a means of cultivating exploratory talk in the classroom. Their materials are targeted at elementary children, but can be adapted for older students as well.

Sylvia Rojas-Drummond and Neil Mercer, “Scaffolding the development of effective collaboration and learning”
Summary of a collaboration between Mexican and British researchers that documents the effectiveness of using exploratory talk strategies to improve collaborative reasoning and learning in the group work-centered classroom.

Neil Mercer and Claire Sams, “Teaching children how to use language to solve maths problems”
Summary of the research behind the interventional program called Thinking Together  and how to proactively make talk-based group activities more effective in developing students’ mathematical reasoning, understanding, and problem-solving.

Monday, July 21, 2014

#TMC14 GWWG: Talking Points Activity – cultivating exploratory talk through a growth mindset activity

This activity is the one I am most excited about bringing to #TMC14 and to the Group Work Working Group. My intention is to blog more about how this goes during the morning sessions. I also hope that participants will blog more about this too and contribute resources to the wiki.

Exploratory talk is the greatest single predictor of whether group work is effective or not, yet most symmetrical classroom talk (peer talk) is either cumulative (positive but uncritical) or disputational (merely trading uncritical disagreements back and forth).

This activity is based on Lyn Dawes’ Talking Points activity but has been adapted for use within a restorative practices framework. It’s a great way to practice circle skills (i.e., respecting the talking piece) and get students to practice NO COMMENT (i.e., trying to score social points rather than focusing on the task at hand).


  • to support students’ exploratory talk skills by pushing them out of cumulative and disputational modes and into a more exploratory talk mode (i.e., speaking, listening, justifying with NO COMMENT)
  • to reveal student thinking about speaking, listening, justifying and about having a growth mindset 
  • to cultivate a growth mindset community

17 minutes

Get students into groups of three.

Talking Points is a timed activity. Groups will have exactly ten minutes to do as many rounds as they can do. For the whole-class debrief at the end, try to keep track of who thought what and why.

Like classroom circles, Talking Points proceeds in rounds. Each “talking point” statement on the list receives three rounds of attention. One person reads the first statement aloud with NO COMMENT. There are then three rounds of speaking and listening. You want these to be “lightning rounds” rather than plodding or deliberate rounds. The Talking Point statements are provocative and designed to stimulate reactions that can be worked with.

10 minutes

ROUND 1 – Go around the group, with each person saying in turn whether they AGREE, DISAGREE, or are UNSURE about the statement AND WHY. Even if you are unsure, you must state a reason WHY you are unsure. NO COMMENT. You’ll be free to change your mind during your turn in the next round.

ROUND 2 – Go around the group, with each person saying whether they AGREE, DISAGREE, or are UNSURE about their own original statement OR about someone else’s statement they just heard AND SAY WHY. NO COMMENT. You are free to change your mind during your turn in the next round.

ROUND 3 – Take a tally of AGREE / DISAGREE / UNSURE and make notes on your sheet. NO COMMENT

Groups should then move on to the next Talking Point.

At the end of ten minutes ring the bell and have groups finish that round. Don’t let the process go on — they need to stop and move on.

2 minutes

At the end of the ten minutes, give students exactly two minutes to fill out the Group Self-Assessment. They will use this during the whole-class debrief and will hand this in for a group grade.

5 minutes

Ask each group to report out about specifics, such as:

Who in your group asked a helpful question and what was it?
Who in your group changed their mind about a Talking Point? How did that occur?
Who in your group encouraged someone else? How did that benefit the conversation?
Who in your group provided an interesting additional idea and what what is?
Who did your group disagree about and why?

I generally choose two or three of these questions and then move on to the actual mathematical group work while the energy level is still high.

Here are links to the first two documents for this activity:

Talking Points handout 1 – talking about talking
Talking Points – Group Self-Assessment

I'll post links to a whole barrelful of the research as soon as I can!

Sunday, July 20, 2014

TMC #14 Group Work Working Group Morning Session – The Game Plan

There is so much that we could focus on that I felt a strong need to narrow things down. TMC morning sessions seem to work best when they are more “master class” than “introduction,” so I am going to keep us aimed in that direction.

So this three-day morning session will NOT be an introduction to using group work. Rather, we will use the three days as an “Advanced Topics in Improving Group Work” session.

I’ll kick things off with a brief overview presentation on the background, research, and framework for these two topics. Then, we will spend the three days we are going to focus our work in two key areas:
We will explore the need to cultivate a culture of ‘exploratory talk’ in our classrooms (as opposed to ‘cumulative’ or ‘disputational’ talk) and practice ways to develop and deploy exploratory talk tasks. Questions we’ll investigate include — What is ‘exploratory talk’? Who has studied it? Why is it important? How does it improve learning? How is it measured? How does it fit into the learning cycle? What is the evidence-based work that’s been done in this area? How can I harness this work in my classroom?  
We will work together on getting better at improvising group task development and deployment Questions we’ll investigate include — What are the major types of group-worthy tasks? What fits where in the learning cycle? Which types are effective for which processes? How can I develop fluency in developing and deploying the different kinds of tasks in my course area and classroom?
We’ll try out different tasks and task types, analyze them, and split up into sub-groups to sketch out new tasks of the various types that fit what we ourselves will be teaching. Then the whole group can act as a “beta test site” for the tasks we are sketching out.

Each day, we’ll begin with some exploratory talk tasks and structures I’ve researched and will share on the web.

I think it would be amazing if we could also come up with a way of categorizing/labeling different types of tasks to give ourselves more helpful information about what tasks are useful for what purposes.

Looking forward to working with you!

Thursday, July 17, 2014

DIY Geometry Vocabulary Game, courtesy of the MTBoS (a collaborative effort)

Through an amazing collaborative effort on Twitter that took, like, all of 15 minutes, the collective hivemind of the #MTBoS came up with a great way to teach/reinforce vocabulary using Maria Anderson's tic-tac-toe style of Block games.

Most of the needed resources are referenced here on my Words into Math blog post.

I just added a bunch of new files to the Math Teacher wiki, including blank vocab cards so the kids can make up their own practice cards.  I make cards in Pages, so I'm also including the PDF and an exported Word doc version.

BLANK TEMPLATE Words into Math Block game cards.pages

BLANK TEMPLATE Words into Math Block game cards.pdf

1-3 Words into Math Block game cards LEVEL 1 SIDE A.doc

1-3 Words into Math Block game cards LEVEL 1 SIDE B.doc

1-3 Words into Math Block game cards LEVEL 1 SIDE B.pages

1-3 Words into Math Block game cards LEVEL 1 SIDE A.pages

Here's a link to the gameboard.

And voilĂ ! A vocab activity for Geometry is born.

When we receive the Oscar for this production, credit should go to Teresa Ryan (@geometrywiz), Julie Reulbach (@jreulbach), Kate Nowak (@k8nowak , aka The High Priestess), Sam Shah (@samjshah), Tina Cardone (@crstn85), Michael Pershan (@mpershan), and if there's room left in the credits, me too.

Monday, July 14, 2014

Life on the Unit Circle - Board Game for Trig Functions

I suppose it was predictable that I would turn the unit circle into a board game as a practice activity, but somehow this still caught me by surprise last night as I was drifting off to sleep. Thank you, deeper wisdom of the unconscious.  :)

This uses the same basic idea as Life on the Number Line, but you can use whatever trig or inverse trig or other practice cards or problems you want to use. Choose your game piece, take turns, and everybody solves whatever problem comes up. Rolling a positive-positive-number or a negative-negative-number on the dice moves your game piece in the counter-clockwise direction (positive angle in standard position) from (0, 1) to start; rolling a positive-negative-number combination moves you in the direction of a negative angle in standard position (clockwise around the circle from wherever you are).

I like this as a practice structure because I try to avoid games that have a strong win-lose association. It also communicates my group work norms of "same problem, same time" and "work in the middle."

You can use the game cards from Trig War (on Sam's blog) or Inverse Trig War (on Jonathan's blog) or from anyone else. I know I plan to. Have kids shuffle them into two piles, one for positive moves and one for negative moves. The point is to do a lot of problems and to get kids used to living on the unit circle. Print the problem cards on colored paper for variety.

I have one new rule, though: whatever point you land on, you have to declare the cosine and sine of that function.

I "score" this as a tournament, requiring each group to do a minimum number of problems, usually a pretty huge number. I keep group scores on a poster or on the white board. I also offer extra credit points for groups that exceed an even more outrageous number of problems. For some reason, the words "extra credit" seem to add a magical flair. I say, who cares as long as kids practice — they're only points!

I buy my plus-minus dice from this seller on eBay and have never had a problem.

Friday, July 11, 2014

Beginner's Mind

Few of us succeed in truly bringing a beginner’s mind to our experience of mathematics. By the time we reach middle school, it is already impossible. We have experiences, beliefs, and opinions about what it takes to do math that have been formed by other people’s experiences, beliefs, and opinions. Students show up in my classes believing — as early as age eleven — that they are good at math or bad at math, that they love math or hate it, prefer decimals over fractions, use a calculator as a defense mechanism and a talisman, and even those who love books believe that word problems are evil. These attitudes get locked in early, and they continue to shape our experiences with math for the rest of our lives.

When I was in first grade, Mrs. Williams gave us each a little muslin drawstring bag of colored wooden blocks and rods. There were little ivory cubes and stubby red rods that were about the same scale as the houses and hotels in a Monopoly set. The apple green rods were just a little bit longer. One, two, three. Each rod got one unit longer, but not wider, than its predecessor. All the way from one to ten. We each kept our little bag in our desk all year long.

I did not know this then, but these are called manipulatives. Mathematical manipulatives. Cuisenaire rods, more specifically. They were invented in the 1920s by Georges Cuisinaire, an imaginative Belgian teacher, and were popularized in the 1950s by the great mathematical educator Caleb Gattegno. As a teacher and as a learner, I have always had a crush on Gattegno. His math pedagogy mirrors the inner development teachings of my root teacher, Fred Orr. Gattegno said, “Only awareness is educable.” Fred said, “Noticing shifts the energy.” When I first encountered those Cuisenaire rods, I could not have known that these two currents of awareness would flow together into a stream that would subtend every aspect of my life.

Those little rods became my friends. I loved the way they felt between my fingers. I loved the smell of the muslin bag and the way they clicked together inside the bag when I took them out during arithmetic lessons or tucked them back into into the darkness of my desk’s inner compartment.

I loved the sound they made when they clattered onto the desk in preparation for our daily lessons. We used them for counting, equivalence, and for modeling mathematical operations. I also used them for personal puppet shows. I traced their shapes on paper with a fat yellow pencil, and I colored in my outlines according to their shapes — white, red, green, blue. Those little blocks cast a long, cool shadow in my mathematical memory. They kept me connected to mathematical wonder even when I felt certain I had no clue about anything mathematical.

Years later, I realized you could buy them on Amazon, and I bought the traditional wooden set. They no longer come with the muslin bag. I cleared off the old oak dining table so I could hear that long-ago sound of the blocks on my desk. It was still exactly the same. I picked up one block or rod at a time and turned it between my fingers. I inspected them. I smelled them. I lined them up: white, red, green. It was one of my madeleine moments.

Before my parents moved away from that old town, I borrowed my mother’s Jeep and drove back to my old school. It was exactly as I had remembered it, only a little bit uglier and smaller. It was after school, and the door was open. I followed the corridor around, past my kindergarten classroom at the first corner that had long ago become the school library. I walked down the linoleum-floored, painted cinder block corridor to the room that had once been Mrs. Williams’ classroom and my own. It was unchanged, except that the blond spinet piano was no longer in the corner. That spot now housed a small cluster of computers.

I wanted to lift the lid of one of the desks to see if there was a drawstring bag of Cuisenaire rods inside.

The rods make me think about beginner’s mind in mathematics. Our minds and emotions get so tangled up and cluttered, it’s not easy to approach math without preconceptions. My first Zen teacher was Keido Les Kaye of Kannon Do. He was the thirteenth monk ordained in America by Shunryu Suzuki, known by most American dharma practitioners as Suzuki Roshi. Suzuki Roshi said, “In the beginner’s mind, there are many possibilities, while in the expert’s mind, there are few.”

This is as true in school mathematics as it is in the study of mindfulness.

As learners, we quickly become experts at either embracing or avoiding math. Our defense mechanisms against shame, humiliation, and confusion become fierce. They harden our hearts. Those of us who suffer from trauma and anxiety around  math come by it honestly. In response to years of competition and sorting and embarrassment, our unconscious minds develop powerful and uniquely personal sets of defense mechanisms. These arise as protective functions in the Self, emerging to shield us against intolerable feelings of panic and confusion and shame.

But there is a different kind of relationship with mathematics that is possible, and it is not only possible for anyone to enter it — it is also essential. It begins with setting aside what we think we know about math, and allowing ourselves to experience it through beginner’s mind — through a mind that is open and self-aware and unselfconscious. It is about setting aside our adult preconceptions for a few moments and allowing ourselves to sink down into the flow of curiosity — the kind of curiosity I remember feeling when I sat on the curb and watched a millipede shuffling along in the ninety-degree New Jersey heat and in the ninety-degree angle between the curb and the gutter, its black legs fluttering along like little windmills, flipping over and over in an articulated lumber, like a deck of cards being shuffled before the magic begins.

Growth Mindset Quote of the Day — 11-Jul-14

"To achieve great things, two things are needed: a plan and not quite enough time."
— Leonard Bernstein